I'm young, but asthmatic enough that I often shoot with Albuterol in my system -- which makes me shake like a leaf, including severe tremors in my hands and arms. I've had to learn to shoot despite the shakes. And I've learned that it is quite possible to shoot a small group while shaking badly. The secret is in the trigger control.
You have to start by accepting the wobble. Don't try to fight it. Fighting against it makes the tremor worse, and also negatively affects your trigger control. You have to allow the shakes to happen and you have to decide not to snatch at the trigger during the brief moments when your sights are perfectly aligned. Snatching at the trigger will make your shots go wild and make your groups embarrassing.
To begin with, without shooting, hold your sights on target and simply observe the area covered by your sights as you shake. That area is your "wobble zone." Chances are that no matter how badly you are shaking, the wobble zone will actually cover less than two inches of actual target at 10 yards, perhaps considerably less. As long as your trigger pull is smooth, your shots will fall within that small wobble zone. If your shots go anywhere outside that small zone, it will be because of trigger control issues, not the result of your shake.
When you fire, concentrate on pulling the trigger back smoothly at the same speed throughout its entire stroke. Never try to grab the magic moment when the sights are "most perfectly" aligned; just pull the trigger smoothly while accepting the wobble zone for what it is. Try not to anticipate the moment the shot will fire.
After the shot has fired, when the trigger gets to its rearmost stopping point, continue to hold the trigger completely to the rear until your sights are lined back up. With the trigger in its rearmost position, count two full seconds, and only then slowly release the trigger. This exaggerated emphasis on follow through really helps avoid jerking shots downward.
HTH.
pax